Generally, motors in electric drive technology are based on the power of a current-carrying conductor in a magnetic field: the Lorentz force, or rather the law of induction.
The permanently excited synchronous motor is used, for example, for many applications. The primary advantages of these motors are the high efficiency, the high transient overload capacity, and excellent controllability, with comparatively compact dimensions.
The prior art is a field-oriented control of three-phase machines. Originally, the (magnetic) field-oriented control was developed in order to be able to control asynchronous machines just as dynamically as direct-current machines. In asynchronous machines, the magnetic field of the rotor is estimated. The stator current is impressed based on the angle of the magnetic field. With the aid of the Park transformation, the stator current may be divided into a field-generating component (id) and a torque-generating component (iq).
The field-oriented control which was originally developed for asynchronous machines is now also being used in permanently excited synchronous machines. Here, the orientation of the magnetic field may be calculated directly from the angle of the rotor. It is also customary to weaken the magnetic field via the current component is in order to be able to achieve higher rotational speeds.
One parameter of a permanently excited synchronous motor is the torque constant KT.M(t)=KT·ig(t)
The approximately proportional relationship between the torque-generating current iq and the torque M enables the good controllability. The current is therefore often used as a controlled variable in order to adjust the desired torque as a target variable.
This approximately proportional relationship is based on the Lorentz force in the current-carrying conductor. If the conductor runs perpendicular to the magnetic field, the following results:F=B·l·I where F is the force, l is the length of the conductor in the magnetic field, I is the current intensity, and B is the magnetic flux density.
Ferromagnetic metal sheets are generally used for conducting the magnetic flux. The advantage of these metal sheets is the good magnetic permeability. One disadvantage of metal sheets is saturation effects at high flux densities.
According to Ampere's law, the magnetic field strength H results from the current, the winding specifications, and the mechanical dimensions of a magnetic circuit without an air gap. A proportional relationship thereby results:H=C1·I 
The constant C1 describes the influence of the winding specifications and the mechanical dimensions.
The flux density B (of the magnetic circuit without an air gap) initially increases approximately proportionally to the current I. In the further progression, the slope decreases due to saturation; thus, the characteristic curve becomes increasingly flat.
If a magnetic circuit having an air gap is considered, the nonlinearity due to saturation decreases considerably.
This configuration, i.e., a magnetic circuit having an air gap, is found in electric motors. In a permanently excited synchronous machine, for example, the torque M(I) does not behave linearly due to saturation. This function is generally ascertained on a torque test stand.
An additional parameter of an electric motor is the winding inductance L.
The inductance is calculated from the flux linkage Ψ and the current I.
  L  =      Ψ    I  
With Ψ=N·A·B, it follows that:
  L  =            N      ·      A      ·      B        I  where N is the winding of the coil, A is an oriented surface, and B is the flux density.
If an inductor having saturation effects is operated about an operating point, the change in the linked flux ΔΨ relative to the change in the current ΔI may differ from the value of the static inductance. For small changes about an operating point, the differential inductance Ldiff results from the increase in the tangent:
      L    diff    =            A      ·      N      ·                        d          ⁢                                          ⁢          B                dI              =          C      ·                        d          ⁢                                          ⁢          B                dH            
The increase in the magnetization characteristic curve, and thus the differential inductance, decreases with increasing stator current.
This effect should be considered when designing the current control circuit, since the differential inductance which is relevant from a control standpoint may definitely decrease to well less than half.
If the change in the differential inductance is not considered, the control loop may become unstable at high currents, or the full control loop bandwidth will not be achieved at low currents.
In the prior art, saturation effects are considered at two points, from a control standpoint.
The setpoint value of the current controller, the reference value, is no longer calculated linearly via the torque constant KT from the setpoint torque, i.e., the target value;
      I    setpoint    =            1              K        T              ·          M      setpoint      rather, a stored, nonlinear characteristic curve is used instead for forming the reference value:Isetpoint=f(Msetpoint)
Generally, experimentally ascertained data points are stored tabularly and are interpolated linearly.
The proportional gain of the current controller Kr may be adjusted with respect to the nonlinear differential winding inductance. The following holds true as a very good approximation:KP(I)=C2·Ldiff(I)
Here as well, it is customary to store the differential inductance or the proportional gain of the current controller in a table as a function of the current.
The approaches according to the prior art have the following disadvantages:
The effects of the magnetic saturation due the stator current are considered at two points. Two tables are stored, which must also be ascertained and parameterized. This means double effort during ascertainment, as well as double effort during the online calculation of the algorithms. An online calculation takes place, for example, during the operation of an electric machine.
Unexamined Patent Application DE 10 2010 003 218 A1 shows a method for controlling and/or regulating a metering pump. Although this unexamined patent application mentions a magnetic flux, it does not specify further which flux is involved: rotor, stator, leakage, etc. The magnetic flux is used as an auxiliary value for describing the torque, without a formula describing a relationship.
Unexamined Patent Application DE 10 2013 207 121 A1 describes a method for how a motor may be operated primarily in a controlled manner: the setpoint currents id and iq are calculated from a torque setpoint value. From them, the necessary voltages vd and vq are also calculated and pre-controlled. This unexamined patent application does not deal with saturation effects.
Patent application DE 26 40 622 C3 describes a method for how the voltage of a DC intermediate circuit may be stabilized in the case of a network failure, in order to be able to accelerate as rapidly as possible when the network returns. During the interruption, the magnetic flux (rotor) of an asynchronous machine can be stabilized. In this patent application, the amplitude of the rotor flux is considered, not the amplitude of the stator flux.
Patent application EP 0 836 270 B1 describes a method for how saturation effects of the q-current may be reduced via an additional field-weakening d-current, so that a higher torque becomes possible. FIG. 16 of the patent application shows the relationship between the torque-generating current iq and the torque. In the saturation region, the torque may be increased via a field-weakening d-current. In reality, this is very small, since the additional d-current must also be applied, and the q-current must therefore generally be reduced. A linearization of the characteristic curve is not discussed.
In the known prior art, the two effects of saturation, i.e., the nonlinear relationship between the current and torque, and the reduction in the winding inductance due to saturation, are considered separately and are compensated for separately. This is not very efficient, more complicated, and more complex in terms of parameterization and in terms of the algorithms.